Fingering instabilities in tissue invasion: an active fluid model

We study theoretically a possible physical mechanism for the formation of multicellular protrusions in carcinoma at the onset of metastasis. We suggest that these patterns may be a consequence of a mechanical instability, reminiscent of the classical viscous fingering instability, which results from tumor growth and cell's active traction. We first develop a simple model for the tissue's traction field, which we use to explore various regimes of instability. We notably show that, for a carcinoma growing in an external environment of comparable mechanical properties, even weak active traction can lead to multicellular protrusions. We also discuss the further evolution of the fingers within this model. Thanks to the simplicity and versatility of the proposed mechanism, we believe our model may be applicable in a wide range of scenarios, and may indeed rationalize fingering phenomena observed in vivo.